Method of recognizing and tracking multiple spatial points

ABSTRACT

The present invention relates to a method of recognizing and tracking multiple spatial points, and more particularly to a method of measuring coordinates of a plurality of point light sources by an optical system comprised of a plurality of 1D optical lens modules and a logical analysis method to achieve the purpose of recognizing and tracking multiple spatial points.

FIELD OF THE INVENTION

The present invention relates to a method of recognizing and trackingmultiple spatial points, and more particularly to a method of measuringcoordinates of a plurality of point light sources by an optical systemcomprised of a plurality of 1D optical lens modules and a logicalanalysis method to achieve the purpose of recognizing and trackingmultiple spatial points.

BACKGROUND OF THE INVENTION

In a method of recognizing and tracking a spatial point as described inU.S. patent application Ser. No. 12,047,159, an embodiment is used forillustrating the method of the patent application. In the method,vertically and horizontally arranged 1D optical lenses are used forcomputing the coordinates of the position of a point light source (or anobject point) according to the position of a line image and a relatedconvergent parameters, but the method is not applicable for a pluralityof point light sources arranged in a specific space as illustrated inthe following examples.

In an 1D vertical focusing lens 1 (which is represented by a shortdouble arrow headed line in FIG. 1( a), and the arrow directionrepresents the focusing direction of the 1D optical lens) as shown inFIG. 1( a), the line image positions of point light sources o₁, o₂disposed at different vertical positions are i_(y1), i_(y2)respectively, such that the 1D optical lens 1 can analyze and recognizethe point light sources o₁, o₂ in the vertical direction. However, thesame line image position i_(y1) is obtained when the point light sourceso₁, o₁′ are both disposed on a plane of Z=C (which is a planeperpendicular to the optical axis Z) and situated on the same horizontalline. In other words, the 1D optical lens 1 cannot analyze and recognizethe point light sources o₁, o₁′ in the horizontal direction.

For the 1D horizontal focusing lens 2 as shown in FIG. 1( b), the pointlight sources o₁, o₂ are disposed at different horizontal positions andtheir line images positions are i_(x1), i_(x2) respectively, such thatthe 1D optical lens 2 can analyze and recognize the point light sourceso₁, o₂ in the horizontal direction. However, the same line imageposition i_(x1) is obtained when the point light sources o₁, o₁′ of the1D horizontal focusing lens 2 are both disposed on a plane of Z=C (whichis a plane perpendicular to the optical axis Z) and situated on the samevertical line. In other words, the 1D optical lens 2 cannot analyze andrecognize the point light sources o₁, o₁′ in the vertical direction.Therefore, if the plurality of point light sources disposed at a planeperpendicular to the optical axis (hereinafter referred to as an opticalaxis perpendicular plane) are arranged at positions perpendicular to thefocusing direction, the images will be superimposed, and the spatialpositions of the plurality of point light sources cannot be recognized.

As described in the aforementioned patent, three 1D optical lensarranged in a fixed space are used, and if any two or more point lightsources are disposed at the optical axis perpendicular plane of any 1Doptical lens and arranged at positions perpendicular to the focusingdirection of that 1D optical lens, the 1D optical lens will lose therecognition function. This result can be shown clearly by the followingtheoretical analysis.

Refer to FIG. 2( a) for the schematic view of the principle of imagingby a 1D vertical focusing lens.

After an object point of a point light source located at P(0,Y_(P),Z_(P)) forms a line image at the position I(0,y_(i),0) by the 1D opticallens 3, the relation between positions of the object point and the lineimage follows the principle of geometric optical imaging as shown in thefollowing equation.

$\begin{matrix}{{\frac{1}{l_{o}} + \frac{1}{l_{i}}} = \frac{1}{f}} & (1)\end{matrix}$

Where l_(o) is the object distance of the point light sourceP(0,Y_(P),Z_(P)), l_(i) is the image distance, and f is the focal lengthof the 1D optical lens 3. In the theory of geometric optical imaging, anon-deviated light exists between the point light sourceP(0,Y_(P),Z_(P)) and the image point I(0,y_(i), 0), and the light passesthrough a geometric center O_(lens) of the 1D optical lens 3. If theobject distance l_(o) is much greater than the image distance l_(i), orl_(o)>>l_(i), then the relation of l_(i)=f can be obtained.

Refer to FIG. 2( b) for the schematic view of the imagingcharacteristics of a 1D vertical focusing lens.

For a point light source arbitrarily disposed at P(0,Y_(P),Z_(P)), atransverse line image is formed by the 1D vertical focusing lens 3 andsituated at a position I(0,y_(l),0) For another arbitrary point lightsource P(X_(P),Y_(P),Z_(P)) situated in the same horizontal direction,the formed image is also a transverse line and situated at the sameposition I(0,y_(i),0). Therefore, P(0,Y_(P),Z_(P)) is defined as anaxial point light source, and P(X_(P),Y_(P),Z_(P)) is defined as aconjugated point light source of P(0,Y_(P), Z_(P)).

Refer to FIG. 2( c) for a schematic view of the characteristics ofimaging of a 1D optical lens in arbitrary focusing direction.

As to the coordinate system O(X,Y,Z), the focusing direction of the 1Dfocusing lens is rotated at an angle θ with respect to axis Z. A newcoordinate system O₁(x,y, z) superimposed on the coordinate systemO(X,Y,Z) is defined, such that the x−y axes are also rotated at an angleθ with respect to axis Z. Therefore, in the new coordinate systemO₁(x,y,z), let P₁(0,y_(P),z_(P)) be an axial point light source and P₁(x_(P),Y_(P),z_(P)) be a conjugated point light source of P₁(0,y_(P),z_(P)) In the coordinate system O(X,Y,Z), the coordinate of P₁(x_(P),y_(P),z_(P)) is P(X_(P),Y_(P),Z_(P)).

Refer to FIG. 2( d) for a schematic view of a 1D optical lens arrangedarbitrarily in the space.

In the world coordinate system O(X,Y,Z), also named as a visual spacecoordinate system, the point light source 8 is disposed at a position(X_(i),Y_(i),Z_(i)), where 1≦i≦N and N is any integer, and thecoordinates (X_(i),Y_(i),Z_(i)) of the point light source P are alsonamed as object point coordinates. As to the coordinates of all pointlight sources, they are called object point group coordinates anddefined as the center coordinates of an object point group as follows:

$\begin{matrix}{{X_{C} = \frac{\sum\limits_{{i = \; 1},\; N}\; X_{i}}{N}};{Y_{C} = \frac{\sum\limits_{{i = \; 1},\; N}\; Y_{i}}{N}};{Y_{C} = \frac{\sum\limits_{{i = \; 1},\; N}\; Z_{i}}{N}}} & (2)\end{matrix}$

The Z-axis of the world coordinate system is rotated at an angle Θ withrespect to Y-axis first, then is rotated at an angle Φ with respect toX-axis, wherein the positive and negative values of the angle aredefined according to the right hand rule. Therefore, the rotated worldcoordinate system can be defined as O″(X″,Y″,Z″). Further, several otherimage coordinate systems O_(j)″(X_(j)″,Y_(j)″Z_(j)″) can be defined, sothat the origin of the image coordinate systemO_(j)″(X_(j)″,Y_(j)″,Z_(j)″) is situated at the position(h_(xj),h_(yj),h_(zj)) of the world coordinate system O″(X″,Y″,Z″). Forsimplicity, FIG. 2( d) only shows the components of h_(xj). Further, a1D vertical focusing lens L_(j) is set on a Z″_(j) axis of the imagecoordinate system O_(j)″(X_(j)″,Y_(j)″,Z_(j)″) and at a position f_(j)from the origin of the image coordinate system, wherein F_(j) is thegeometric center of the 1D optical lens L_(j), and f _(j) is the focallength. Further, the image coordinate system O_(j)″(X_(j)″,Y_(j)″,Z_(j)″) is rotated at an angle θ_(j) with respect to the Y_(j)″ axisfirst, and then is rotated at an angle ρ_(j) with respect to the Z″_(j)axis, wherein the positive and negative values of the angle are definedaccording to the right hand rule. Therefore, the rotated imagecoordinate system can be defined as O_(j)″(X_(j)″,Y_(j)″,Z_(j)″). Letthe object distance of the point light source 4 be much greater than thefocal length f_(i), and the plane of the focal point becomes an imageplane situated on the plane X_(j)″−Y_(j)″ and Z_(j)″=0 of the imagecoordinate system O_(j)″(X_(j)″,Y_(j)″,Z_(j)″). In the world coordinatesystem O″(X″,Y″,Z″),the point light source P _(i) is situated at theposition P _(i)″(X_(i)″,Y_(i)″,Z_(i)″), and in the image coordinatesystem O_(j)″(X_(j)″,Y_(j)″,Z_(j)″) the point light source Piis situatedat the position P _(ij)(x_(oij),y_(oij),z_(oij)). In the imagecoordinate system O_(j)″(X_(j)″,Y_(j)″,Z_(j)″), let the point lightsource P _(ij)(x_(oij),y_(oij),z_(oij)) be the conjugated point lightsource and P_(ij)(0,Y_(oij),z_(oij)) be the axial point light source.Then the line image position of P_(ij)(0,y_(oij),z_(oij)) is situated atI_(ij)(0,y_(sij),0), and their geometric optical relation is givenbelow:

$\begin{matrix}{y_{oij} = {{- \frac{z_{oij} - f_{j}}{f_{j}}}y_{sij}}} & (3)\end{matrix}$

According to the relation of coordinate transformation between the imagecoordinate system O_(j)″(X_(j)″,Y_(j)″,Z_(j)″) and the world coordinatesystem O(X,Y,Z) and the spatial geometric arrangement of the point lightsources in the world coordinate system O(X,Y,Z), the necessary quantityof 1D optical lenses L_(j) can be derived and the coordinate(X_(i),Y_(i),Z_(i)) of each point light source P _(i) in the worldcoordinate system O(X,Y,Z) can be calculated. The derivation andcalculation are discussed as follows:

The relation of coordinate transformation between the image coordinatesystem O_(j)″(X_(j)″,Y_(j)″,Z_(j)″) and the world coordinate systemO(X,Y,Z) is given below:

$\begin{matrix}{{\begin{pmatrix}X_{i} \\Y_{i} \\Z_{i}\end{pmatrix} = {{{R_{j}\left( {\Theta,\Phi,\theta_{j},\rho_{j}} \right)}\begin{pmatrix}x_{oij} \\y_{oij} \\z_{oij}\end{pmatrix}} + \begin{pmatrix}h_{xj} \\h_{yj} \\h_{zj}\end{pmatrix}}}{Where}} & (4) \\{{{R_{j}\left( {\Theta,\Phi,\theta_{j},\rho_{j}} \right)} = \begin{pmatrix}R_{j\; 11} & R_{j\; 12} & R_{j\; 13} \\R_{j\; 21} & R_{j\; 22} & R_{j\; 23} \\R_{j\; 31} & R_{j\; 32} & R_{j\; 33}\end{pmatrix}}{and}} & (5) \\{{R_{j\; l\; m} \equiv {f\left( {\Theta,\Phi,\theta_{j},\rho_{j}} \right)}},{1 \leq l \leq 3},{1 \leq m \leq 3}} & (6)\end{matrix}$

R_(jlm) is a function of Θ,Φ,θ_(j), ρ_(j). With the matrix operation, P_(ij)(x_(oij),y_(oij),z_(oij)) can be computed as follows:

$\begin{matrix}{{\begin{pmatrix}x_{oij} \\y_{oij} \\z_{oij}\end{pmatrix} = {{r_{j}\left( {\Theta,\Phi,\theta_{j},\rho_{j}} \right)}\left\lbrack {\begin{pmatrix}X_{i} \\Y_{i} \\Z_{i}\end{pmatrix} - \begin{pmatrix}h_{xj} \\h_{yj} \\h_{zj}\end{pmatrix}} \right\rbrack}}{{where},}} & (7) \\\begin{matrix}{{r_{j}\left( {\Theta,\Phi,\theta_{j},\phi_{j}} \right)} = {R_{j}\left( {\Theta,\Phi,\theta_{j},\phi_{j}} \right)}^{- 1}} \\{= \begin{pmatrix}R_{j\; 11} & R_{j\; 12} & R_{j\; 13} \\R_{j\; 21} & R_{j\; 22} & R_{j\; 23} \\R_{j\; 31} & R_{j\; 32} & R_{j\; 33}\end{pmatrix}^{- 1}} \\{{= \begin{pmatrix}r_{j\; 11} & r_{j\; 12} & r_{j\; 13} \\r_{j\; 21} & r_{j\; 22} & r_{j\; 23} \\r_{j\; 31} & r_{j\; 32} & r_{j\; 33}\end{pmatrix}},}\end{matrix} & (8)\end{matrix}$

Expand Equation (7) to obtain

$\begin{matrix}{\begin{pmatrix}x_{oij} \\y_{oij} \\z_{oij}\end{pmatrix} = \begin{pmatrix}{{r_{j\; 11}\left( {X_{i} - h_{xj}} \right)} + {r_{j\; 12}\left( {Y_{i} - h_{yj}} \right)} + {r_{j\; 13}\left( {Z_{i} - h_{zj}} \right)}} \\{{r_{j\; 21}\left( {X_{i} - h_{xj}} \right)} + {r_{j\; 22}\left( {Y_{i} - h_{yj}} \right)} + {r_{j\; 23}\left( {Z_{i} - h_{zj}} \right)}} \\{{r_{j\; 31}\left( {X_{i} - h_{xj}} \right)} + {r_{j\; 32}\left( {Y_{i} - h_{yj}} \right)} + {r_{j\; 33}\left( {Z_{i} - h_{zj}} \right)}}\end{pmatrix}} & (9)\end{matrix}$

Substitute Y_(oij) and z_(oij) of Equation (9) into Equation (3) toobtain

(f _(j) r _(j21) +r _(j31) y _(sij))X _(i)+(f _(j) r _(j22) +r _(j32) y_(sij))Y _(i)+(f _(j) r _(j23) +r _(j33) y _(sij))Z _(i)=(f _(j) r_(j21) +r _(j31) y _(sij))h _(xj)+(f _(j) r _(j22) +r _(j32) Y _(sij))h_(yj)+(f _(j) r _(j23) +r _(j33) y _(sij))h _(zj) +f _(j) y _(sij)  (10)

where, 1≦i≦N, 1≦j≦M, and N is the number of point light sources and M isthe number of 1D optical lenses.

For N point light sources situated at (X_(i),Y_(i),Z_(i)), 3Nindependent equations are required for solving the coordinates(X_(i),Y_(i),Z_(i)) of all of N point light sources. Therefore, at leastthree 1D optical lenses (M=3) are required and installed in the properfocusing directions to satisfy the conditions of the 3N independentequations. However, if the arranged positions of the plurality of pointlight sources as shown in FIGS. 1( a) and 1(b) are conjugated, asuperimposition will occur. Therefore, the condition of the 3Nindependent equations cannot be satisfied, and the coordinates of Npoint light sources cannot be obtained. As a result, the effect of theforegoing patented technology cannot be achieved.

For an independent solution of Equation (10), we have to avoid theaforementioned image superimposition. In other words, for N freelymoving point light sources, the coordinates (X_(i),Y_(i),Z_(i)) of eachpoint light source can be calculated only when N independent andrecognizable images y_(sij) are obtained from each 1D optical lensL_(j). For multiple point light sources arranged in a specific positionor movement, a specific arrangement for the directions of the 1D opticallenses, or increasing the number of 1D optical lenses is an effectiveway to obtain the coordinates of multiple point light sources. Howeverit is not a good solution for multiple freely moving point light sourceswhich may easily cause the issue of the image superimposition. Accordingto Equations (9) and (3), the image superimposition can be eliminated ifthe value r_(j)(Θ,Φ,θ_(j),ρ_(j)) is varied properly. In other words, therelation of the coordinate transformed is changed to remove the imagesuperimposition.

SUMMARY OF THE INVENTION

Therefore, it is a primary objective of the present invention toovercome the shortcomings of the prior art and provide a capability ofrecognizing spatial positions of multiple point light sources. Formultiple point light sources arranged in a specific position or movementor in a freely moving condition, an optical system comprised of aplurality of 1D optical lenses and a logical analysis method are usedfor eliminating the image superimposition and computing the coordinatesof multiple point light sources, so as to achieve the purpose ofrecognizing and tracking the multiple point light sources in the visualspace.

The above and other objects, features and advantages of the presentinvention will become apparent from the following detailed descriptiontaken with the accompanying drawing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1( a) is a schematic view of the principle of imaging by a 1Dvertical focusing lens;

FIG. 1( b) is a schematic view of the principle of imaging by a 1Dhorizontal focusing lens;

FIG. 2( a) is a schematic view of the principle of imaging by a 1Dvertical focusing lens;

FIG. 2( b) is a schematic view of the characteristic imaging of avertical 1D focusing lens;

FIG. 2( c) is a schematic view of the characteristic imaging of a 1Doptical lens in arbitrary focusing direction;

FIG. 2( d) is a schematic view of a 1D optical lens arranged arbitrarilyin the space;

FIG. 3( a) is a schematic view of an optical system in accordance with afirst preferred embodiment of the present invention;

FIG. 3( b) is a schematic view of an optical system in accordance with asecond preferred embodiment of the present invention;

FIG. 3( c) is a schematic view of an optical system in accordance with athird preferred embodiment of the present invention;

FIG. 3( d) is a schematic view of an optical system in accordance with afourth preferred embodiment of the present invention;

FIG. 3( e) is a schematic view of an optical system in accordance with afifth preferred embodiment of the present invention;

FIG. 4 is a schematic view of an optical system in accordance with asixth preferred embodiment of the present invention; and

FIG. 5 is a schematic view of an optical system in accordance with aseventh preferred embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

To make it easier for our examiner to understand the characteristics,objects and functions of the present invention, we use preferredembodiments and related drawings for the detailed description of thepresent invention as follows.

Embodiment 1

Refer to FIG. 3( a) for a schematic view of an optical system inaccordance with a third preferred embodiment of the present invention.

In this embodiment, a variable number N of freely moving point lightsources P _(i)(X_(i),Y_(i),Z_(i)) with an arbitrary wavelength exists ina visual space, and an optical system of this embodiment is comprised ofthree 1D focusing lenses L₁{grave over ( )}L₂{grave over ( )}L₃ with adifferent focal length f_(j) (where, 1≦j≦3) or an equal focal length f.For simplicity, the equal focal length f is used for the illustration inthe figures. For a world coordinate system O(X,Y,Z), the origins of thethree freely rotating image coordinate systems O₁(X₁,Y₁,Z₁),O₂(X₂,Y₂,Z₂), O₃(X₃,Y₃,Z₃) are disposed at any fixed positions(h_(x1),h_(y1),h_(z1)), (h_(x2),h_(y2), h_(z2)), (h_(x3),h_(y3),h_(z3))or disposed along any one of the transverse axes. For simplicity, thesymmetric positions along the X-axis are used for the illustration. Inother words, the origins of the three image coordinate systemsO₁(X₁,Y₁,Z₁), O₂(X₂,Y₂,Z₂), O₃(X₃,Y₃,Z₃) are disposed at fixed positions(−h,0,0), (0,0,0), (h,0,0).

At the initial state, the X_(j), Y_(j), Z_(j) axes (where, 1≦j≦3) of thethree image coordinate systems O₁(X₁,Y₁,Z₁), O₂(X₂,Y₂,Z₂), O₃(X₃,Y₃,Z₃)are parallel to the X, Y, Z axes of the world coordinate system O(X,Y,Z)respectively. In the three image coordinate systems O₁(X₁,Y₁,Z₁),O₂(X₂,Y₂,Z₂), O₃(X₃,Y₃,Z₃), the three 1D focusing lenses L₁{grave over ()}L₂{grave over ( )}L₃ are installed at positions (0,0,f) along theZ_(j) axis, and their focusing directions are parallel to the Y_(j)axis. Further, three 1D image sensor S₁{grave over ( )}S₂{grave over ()}S₃ having M×1 sensing pixels are disposed separately and fixed at theorigin of each of the three image coordinate systems O₁(X₁,Y₁,Z₁),O₂(X₂,Y₂,Z₂), O₃(X₃,Y₃,Z₃) respectively, and the direction of the longaxis of each sensor is parallel to the focusing direction of the 1Dfocusing lens L₁{grave over ( )}L₂{grave over ( )}L₃. If another opticallens module is added to a rear end of the 1D focusing lens L₁{grave over( )}L₂{grave over ( )}L₃ to correct the aberrations, such that the imageis rotated by 90°, then the direction of the long axis of the 1D imagesensor S₁{grave over ( )}S₂{grave over ( )}S₃ is perpendicular to thefocusing direction of the 1D focusing lens L₁{grave over ( )}L₂{graveover ( )}L₃. Since the optical characteristics are the same, the presentinvention is not limited to the image rotation of 90° only, and thussuch rotation will not be described here.

The world coordinate system O(X,Y,Z) may have three types of angularrotations, respectively a rotation of an arbitrary angle Θ with respectto the Y-axis, a rotation of an arbitrary angle Φ with respect to theX-axis, and a rotation of an arbitrary angle Ω with respect to theZ-axis. Therefore, any rotation with the angle of Θ, Φ, Ω of the worldcoordinate system O(X,Y,Z) can rotate the axis of X_(j), Y_(j), Z_(j) ofthe three image coordinate systems O₁(X₁,Y₁,Z₁), O₂(X₂,Y₂,Z₂),O₃(X₃,Y₃,Z₃) at the same time to change the direction of the 1D focusinglens L₁{grave over ( )}L₂{grave over ( )}L₃. Further, the three imagecoordinate systems O₁(X₁,Y₁,Z₁), O₂(X₂,Y₂,Z₂), O₃(X₃,Y₃,Z₃) may have twotypes of angular rotations, respectively a rotation of an arbitraryangle θ_(j) with respect to the Y_(j) axis and a rotation of anarbitrary angle ρ_(j) with respect to the Z_(j) axis σ_(j) angle.Therefore, the image coordinate system O_(j)(X_(j),Y_(j),Z_(j)) can berotated to an angle θ_(j), ρ_(j) to drive the 1D focusing lens L_(j) and1D sensor S_(j) to rotate at the same time. Regardless of the type ofthe angular rotation, the relative angle between the focusing directionof the 1D focusing lens L_(j) and the direction of the long axis of the1D sensor S_(j) remains unchanged.

As described above, if an image superimposition occurs, the values ofthe angles (θ_(j),ρ_(j)) are changed appropriately to eliminate theimage superimposition, and compute the object coordinates of the pointlight source P _(i)(X_(i),Y_(i),Z_(i)). Further, the center coordinates(X_(C),Y_(C),Z_(C)) of the object point group are computed, and theangles (Θ,Φ) are changed to achieve the purpose of tracking the centerof object point group. The logical analysis method comprises thefollowing steps:

Step 1: Set the initial value of each angle (Ω,Θ,Φ,θ_(j),ρ_(j)) to anarbitrary value, preferably equal to (Ω=0°, Θ=0°,Φ=0°), or change andrecord the angles (Θ,Φ) to align the Z-axis with (X_(C),Y_(C),Z_(C)), ifthe center coordinates (X_(C),Y_(C),Z_(C)) of the object point group areknown.

Step 2: Read the number N of point light sources P_(i)(X_(i),Y_(i),Z_(i))

Step 3: Read all images of the 1D optical lenses L_(j), and obtain thenumber Nj of the line image and the coordinates Y_(sij) of the lineimage by an imaging process.

Step 4: Change and record the angle ρ_(j) or θ_(j) and go to Step 3, ifthe number Nj is not equal to N. Go to Step 5, if the number Nj is equalto N.

Step 5: Find the corresponding line image (y_(si1),y_(si2),y_(si3)) ofthe point light source P _(i)(X_(i),Y_(i),Z_(i)), and compute and outputan object point coordinate (X_(i),Y_(i),Z_(i)) according to Equation(10).

Step 6: Compute and output the center coordinates (X_(C),Y_(C),Z_(C)) ofthe object point group according to Equation (2).

Step 7: Change and record the angle (Θ,Φ) to align the Z-axis with(X_(C),Y_(C),Z_(C)) to achieve the purpose of tracking the object pointgroup.

Step 8: Return to Step 2.

Embodiment 2

Refer to FIG. 3( b) for a schematic view of an optical system inaccordance with a second preferred embodiment of the present invention.

The assembly of the optical system of the second preferred embodiment issubstantially the same as that of the first preferred embodiment, exceptθ₁=θ₂=θ₃=0° and the focusing directions of the three 1D focusing lensesL₁{grave over ( )}L₂{grave over ( )}L₃ are set at an angle of ρ₁=90°,ρ₂=0° and ρ₃=90° respectively. Therefore, the direction of the long axisof the three 1D image sensors S₁{grave over ( )}S₂{grave over ( )}S₃ isset parallel to the of focusing direction of the three 1D focusinglenses L₁{grave over ( )}L₂{grave over ( )}L₃. As described above, if animage superimposition occurs, the value of the angle ρ_(j) is changed toeliminate the image superimposition, and compute the object pointcoordinates (X_(i),y_(i),Z_(i)) of point light sources P_(i)(X_(i),Y_(i),Z_(i)). In addition, the center coordinates(X_(C),Y_(C),Z_(C)) of the object point group is computed, and theangles (Θ,Φ) are changed to achieve the purpose of tracking the objectpoint group. The logical analysis method comprises the following steps:

Step 1: Set the initial value of each angle (Ω,Θ,Φ,θ_(j),ρ_(j)) to(θ₁=θ₂=0°,θ₃=0°) and (ρ₁=90°,ρ₂₌₀°,ρ₃₌₉₀°), and (Ω,Θ,Φ) can be any angleand preferably equal to (Ω=0°,Θ=0°,Φ=0°). Change and record the angle(Θ,Φ) such that the Z-axis aligns with (X_(C),Y_(C),Z_(C)), if thecenter coordinates (X_(C),Y_(C),Z_(C)) of the object point group areknown.

Step 2: Read the number N of point light sources P_(i)(X_(i),Y_(i),Z_(i))

Step 3: Read all images of 1D optical lenses L_(j), and obtain thenumber Nj of the line image and the coordinates y_(sij) of the lineimage by an imaging process.

Step 4: Change and record the angle ρ_(j) if the number Nj is not equalto N, and then go to Step 3. If the number Nj is equal to N, then go toStep 5.

Step 5: Find the corresponding line image (y_(si1),y_(si2),y_(si3)) ofthe point light source P _(i)(X_(i),Y_(i),Z_(i)), and compute and outputan object point coordinate (X_(i),Y_(i),Z_(i)) according to Equation(10).

Step 6: Compute and output the center coordinates (X_(C),Y_(C),Z_(C)) ofthe object point group according to Equation (2).

Step 7: Change and record the angle (Θ,Φ) to align the Z-axis with(X_(C),Y_(C),Z_(C)) to achieve the purpose of tracking the object pointgroup.

Step 8: Return to Step 2.

Embodiment 3

Refer to FIG. 3( c) for a schematic view of an optical system inaccordance with a third preferred embodiment of the present invention.

The assembly of the optical system of the third preferred embodiment issubstantially the same as that of the second preferred embodiment,except θ₁=θ, θ₂=0, θ₃=−θ, and the Z_(j) coordinates of the three imagecoordinate systems O₁(X₁,Y₁,Z₁), O₂(X₂,Y₂,Z₂), O₃(X₃,Y₃,Z₃) areintersected at a point which is the convergent pointV(X_(V),Y_(V),Z_(V)). The coordinates V(X_(V),Y_(V),Z_(V)) of theconvergent point can be computed according to the angles Θ, Φ and θ.Further, the focusing directions of the three 1D focusing lensesL₁{grave over ( )}L₂{grave over ( )}L₃ are at ρ₁=90°, ρ₂=0° and ρ₃=90°respectively. Therefore, the directions of the long axes of the three 1Dimage sensors S₁{grave over ( )}S₂{grave over ( )}S₃ are parallel to thefocusing directions of the three 1D focusing lenses L₁{grave over ()}L₂{grave over ( )}L₃ respectively. As described above, if an imagesuperimposition occurs, the value of the angle ρ_(j) is changedappropriately to eliminate the image superimposition and compute the ofobject point coordinates (X_(i),Y_(i),Z_(i)) of the point light source P_(i)(X_(i),Y_(i),Z_(i)). In addition, the center coordinates of theobject point group are computed, and the angles (Θ,Φ) are changed toachieve the purpose of tracking the object point group. The logicalanalysis method comprises the following steps:

Step 1: Set the initial value of each angle (Ω,Θ,Φ,θ_(j),ρ_(j)) to(θ₁=θ, θ₂=0°,θ₃=−θ) and (ρ₁=90°,ρ₂=0°,ρ₃=90°), and the angles (Ω,Θ,Φ)are arbitrary and preferably equal to (Ω=0°,Θ=0°,Φ=0°), or change andrecord the angles (Θ,Φ) to align the Z-axis with (X_(C),Y_(C),Z_(C)), ifthe center coordinates (X_(C),Y_(C),Z_(C)) of the object point group areknown.

Step 2: Read the number N of point light sources P_(i)(X_(i),Y_(i),Z_(i)).

Step 3: Read images of all 1D optical lenses L_(i) and obtain the numberNj of the line image and the coordinates y_(sij) of the line image by animaging process.

Step 4: Change and record the angle ρ_(j) angle and go to Step 3, if thenumber Nj is not equal to N. If the number Nj is equal to N, go to Step5.

Step 5: Find the corresponding line image (y_(si1),y_(si2),y_(si3)) ofthe point light source (and compute and output an object pointcoordinate (X_(i),Y_(i),Z_(i)) according to Equation (10).

Step 6: Compute and output the center coordinates (X_(C),Y_(C),Z_(C)) ofthe object point group according to Equation (2).

Step 7: Change and record the angle (Θ,Φ) to align the Z-axis with(X_(C),Y_(C),Z_(C)) to achieve the purpose of tracking the object pointgroup.

Step 8: Return to Step 2.

Embodiment 4

Refer to FIG. 3( d) for a schematic view of an optical system inaccordance with a fourth preferred embodiment of the present invention.The assembly of the optical system of the fourth preferred embodiment issubstantially the same as that of the third preferred embodiment, exceptwhen an image superimposition occurs, the value of the angle Ω ischanged to eliminate the image superimposition, and calculate the objectpoint coordinates (X_(i),Y_(i),Z_(i)) of the point light sources P_(i)(X_(i), Y_(i),Z_(i)). The center coordinates of the object pointgroup are computed and the angles (Θ,Φ) are changed to achieve thepurpose of tracking the object point group. The logical analysis methodcomprises the following steps:

Step 1: Set the initial value of each angle (Ω,Θ,Φ,θ_(j),ρ_(j)) to(θ₁=θ,θ₂=0°,θ₃=−θ) and (ρ₁=90°,ρ₂=0°=ρ₃=90°), and the angles (Ω,Θ,Φ) arearbitrary and preferably equal to (Ω=0°,Θ=0°,Φ=0°), or change and recordthe angles (Θ,Φ) to align the Z-axis with (X_(C),Y_(C),Z_(C)) if thecenter coordinates (X_(C),Y_(C),Z_(C)) of the object point group areknown.

Step 2: Read the number N of point light sources P_(i)(X_(i),Y_(i),Z_(i)).

Step 3: Read images of all 1D optical lenses L_(j), and obtain thenumber Nj of the line image and the coordinates y_(sij) of the lineimage by an imaging process.

Step 4: Change and record the angle Ω and go to Step 3, if the number Njis not equal to N. Go to Step 5, if the number Nj is equal to N.

Step 5: Find the corresponding line image (y_(sij),y_(si2),y_(si3)) ofthe point light source P _(i)(X_(i),Y_(i),Z_(i)), and compute and outputan object point coordinate (X_(i),Y_(i),Z_(i)) according to Equation(10).

Step 6: Compute and output the center coordinates (X_(C),Y_(C),Z_(C)) ofthe object point group according to Equation (2).

Step 7: Change and record the angle (Θ,Φ) to align the Z-axis with(X_(C),Y_(C),Z_(C)) to achieve the purpose of tracking the object pointgroup.

Step 8: Return to Step 2.

Embodiment 5

Refer to FIG. 3( e) for a schematic view of an optical system inaccordance with a fifth preferred embodiment of the present invention.

The assembly of the optical system of the fifth preferred embodiment issubstantially the same as that of the fourth preferred embodiment,except the angle Ω is rotated at an angular speed ω_(o). The logicalanalysis method comprises the steps of:

Step 1: Set the initial value of each angle (Θ,Φ,θ_(j),ρ_(j)) to(θ₁=θ,θ₂=0°, θ₃=−θ) and (ρ₁=90°,ρ₂=0°,ρ₃=90°), and the angles (Θ,Φ) arearbitrary and preferably equal to (Θ=0°,Φ=0°), or change and record theangles (Θ,Φ) to align the Z-axis with (X_(C),Y_(C),Z_(C)), if the centercoordinates (X_(C),Y_(C),Z_(C)) of the object point group are known(Θ,Φ). Finally, the angle Ω is rotated with an angular speed ω_(o).

Step 2: Read the number N of point light sources P_(i)(X_(i),Y_(i),Z_(i))

Step 3: Read the angle Ω and images of all 1D optical lenses L_(j), andobtain the number Nj of line image and the coordinates y_(sij) of theline image by an imaging process.

Step 4: Go to Step 3 if the number Nj is not equal to N. Go to Step 5 ifthe number Nj is equal to N.

Step 5: Find the corresponding line image (y_(si1),y_(si2),y_(si3)) ofthe point light source P _(i)(X_(i),Y_(i),Z_(i)), and compute and outputan object point coordinate (X_(i),Y_(i),Z_(i)) according to Equation(10).

Step 6: Compute and output the center coordinates (X_(C),Y_(C),Z_(C)) ofthe object point group according to Equation (2).

Step 7: Change and record the angle (Θ,Φ) to align the Z-axis with(X_(C),Y_(C),Z_(C)) to achieve the purpose of tracking the object pointgroup.

Step 8: Return to Step 2.

Embodiment 6

Refer to FIG. 4 for a schematic view of an optical system in accordancewith a sixth preferred embodiment of the present invention.

The characteristics of the assembly of the optical system of the sixthpreferred embodiment is substantially the same as those of the first tofifth preferred embodiments, except the number of 1D focusing lenses isgreater than 3. For simplicity, only four 1D focusing lenses are usedfor the illustration here.

Refer to FIG. 5 for a schematic view of an optical system in accordancewith a seventh preferred embodiment of the present invention.

The optical system in accordance with the seventh preferred embodimentis comprised of four 1D focusing lenses A′±2‘o’±4 and four 1D imagesensors S₁{grave over ( )}S₂{grave over ( )}S₃ The four 1D focusinglenses L₁{grave over ( )}L₂{grave over ( )}L₃ have focal lengthsf₁{grave over ( )}f₂{grave over ( )}f₃{grave over ( )}f₄ respectively.In the world coordinate system O(X,Y,Z), the origins of the imagecoordinate systems O₁(X₁,Y₁,Z₁) O₂(X₂,Y₂,Z₂), O₃(X₃,Y₃,Z₃), O₄(X₄,Y₄,Z₄)are disposed at positions (0,h,0), (0,0,0), (−H,0,H), (H,0,H)respectively, and the orientating angles are θ₁=0°, θ₂=0°,θ₃90°,θ₄=−90°and ρ₁=90°,ρ₂₌₀°,ρ₃=90°,ρ₄₌₉₀°. Further, the logical analysis method ofthe seventh preferred embodiment is the same as those of the first tofifth preferred embodiments.

In summation of the description above, the technical characteristics ofthe method of the invention and each preferred embodiment are disclosedfully to demonstrate the purpose and effects of the present invention,and the invention complies with the requirements of patent application,and thus is duly filed for patent application.

While the invention has been described by means of specific embodiments,numerous modifications and variations could be made thereto by thoseskilled in the art without departing from the scope and spirit of theinvention set forth in the claims.

1. A method of recognizing and tracking multiple spatial points,comprising: a plurality of point light sources, each being capable ofmoving freely, having an arbitrary wavelength and a variable quantity ofN point light sources; an optical system, comprised of a plurality of 1Dfocusing lens modules; and a logical analysis method, for eliminating animage superimposition phenomenon and performing a computation to obtaincoordinates of object points of the plurality of point light sources. 2.The method of recognizing and tracking multiple spatial points of claim1, wherein the plurality of point light sources are an active pointlight source capable of emitting point scattering lights or a passivepoint light source, which reflects a point light source.
 3. The methodof recognizing and tracking multiple spatial points of claim 1, whereinthe 1D focusing lens module is comprised of a 1D focusing lens and arectangular 1D image sensor.
 4. The method of recognizing and trackingmultiple spatial points of claim 1, wherein the 1D focusing lens moduleis comprised of a 1D focusing lens, an aberration correction lensmodule, and a rectangular 1D image sensor.
 5. The method of recognizingand tracking multiple spatial points of claim 1, wherein the opticalsystem is comprised of three 1D focusing lens modules.
 6. The method ofrecognizing and tracking multiple spatial points of claim 1, wherein theoptical system is comprised of at least four 1D focusing lens modules.7. The method of recognizing and tracking multiple spatial points ofclaim 3, wherein the 1D focusing lens has a focusing direction same asthe direction along the longer axis of the 1D image sensor.
 8. Themethod of recognizing and tracking multiple spatial points of claim 4,wherein the 1D focusing lens has a focusing direction same as orperpendicular to the direction along the longer axis of the 1D imagesensor.
 9. The method of recognizing and tracking multiple spatialpoints of claim 5 or 6, wherein the 1D focusing lens modules areinstalled at arbitrary positions in the visual space.
 10. The method ofrecognizing and tracking multiple spatial points of claim 5 or 6,wherein the focusing directions of 1D focusing lenses modules areinstalled in arbitrary orientation in the visual space.
 11. The methodof recognizing and tracking multiple spatial points of claim 5 or 6,wherein the 1D focusing lens modules have arbitrary focal lengths orequal focal lengths.
 12. The method of recognizing and tracking multiplespatial points of claim 5 or 6, wherein all 1D focusing lens modules areinstalled at positions along the transverse axis of the visual spacecoordinate system and equidistant with each other, and arrangedsymmetrically with the origin of the visual space coordinates.
 13. Themethod of recognizing and tracking multiple spatial points of claim 1,wherein the logical analysis method comprises: an initial setting step,for setting and recording an initial value of each angle(Ω,Θ,Φ,θ_(j),ρ_(j)), and reading the number N of point light sources P_(i)(X_(i),Y_(i),Z_(i)); an image processing step, for reading images ofall 1D optical lenses L_(j), and obtaining the number Nj of the lineimage and the coordinates Y_(sij) of the line image; an imagesuperimposition eliminating step, for eliminating an imagesuperimposition by changing the focusing directions of 1D focusinglenses modules, if the image superimposition occurs and the number Nj ofthe line image of the lenses L_(j) is not equal to N; an imagecorresponding to an object point coordinate computing step, forcomputing the object point coordinates (X_(i),Y_(i),Z_(i)) after findingthe corresponding point image (y_(sij),y_(si2),y_(si3)) of the pointlight sources P _(i)(X_(i),Y_(i),Z_(i)) by a corresponding logic; and anobject point group tracking step, for changing the angle of the opticalaxis of the optical system after computing the center coordinates(X_(C),Y_(C),Z_(C)) of the object point group, such that the opticalaxis is aligned with the center coordinates of the object point group toachieve the purpose of tracking the object point group.
 14. The methodof recognizing and tracking multiple spatial points of claim 13, whereinthe initial setting step sets the initial values of (Ω,Θ,Φ,θ_(j),ρ_(j)),and the values of (Ω,Θ,Φ,θ_(j),ρ_(j)) are arbitrary, or the values of(Ω,Θ,Φ) are set to (Ω=0°,Θ=0°,Φ=0°), and if the center coordinates(X_(C),Y_(C),Z_(C)) of the object point group are known, the angles(Θ,Φ) are changed and recorded, so that the Z-axis aligns with(X_(C),Y_(C),Z_(C)).
 15. The method of recognizing and tracking multiplespatial points of claim 13, wherein the initial values of(Ω,Θ,Φ,θ_(j),ρ_(j)) are set, and (θ_(j),ρ_(j)) are set to(0₁=0°,0₂=0°,0₃=0°) and (ρ₁=90°,ρ₂=0°, ρ₃=90°) when the number of the 1Dfocusing lens module is three.
 16. The method of recognizing andtracking multiple spatial points of claim 13, wherein the initial valuesof (Ω,Θ,Φ,θ_(j),ρ_(j)) are set, and (θ_(j),ρ_(j)) are set to(θ₁=θ,θ₂=0°,θ₃=−θ) (ρ₁=90°,ρ₂=0°,ρ₃=90°), and θ≧0° when the number ofthe 1D focusing lens module is three.
 17. The method of recognizing andtracking multiple spatial points of claim 13, wherein the imagesuperimposition eliminating step is achieved by adjusting one of theangles ρ_(j),θ_(j), and Ω.
 18. The method of recognizing and trackingmultiple spatial points of claim 13, wherein the image superimpositioneliminating step is achieved by rotating the angle Ω with a constantangular velocity.
 19. The method of recognizing and tracking multiplespatial points of claim 13, wherein the object point coordinates of thepoint light sources P _(i)(X_(i),Y_(i),Z_(i)) is computed by(f _(j) r _(j21) +r _(j31) y _(sij))X _(i)+(f _(j) r _(j22) +r _(j32) ,y_(sij))Y _(i)+(f _(j) r _(j23) +r _(j33) y _(sij))Z _(i)=(f _(j) r_(j21) +r _(j31) y _(sij))h _(xj)+(f _(j) r _(j22) +Y _(sij))h _(yj)+(f_(j) r _(j23) +r _(j33) y _(sij))h _(zj) +f _(j) y _(sij)
 20. The methodof recognizing and tracking multiple spatial points of claim 13, whereinthe center coordinates (X_(C),Y_(C),Z_(C)) of the object point group iscomputed by${X_{C} = \frac{\sum\limits_{{i = \; 1},\; N}\; X_{i}}{N}};{Y_{C} = \frac{\sum\limits_{{i = \; 1},\; N}\; Y_{i}}{N}};{Y_{C} = {\frac{\sum\limits_{{i = \; 1},\; N}\; Z_{i}}{N}.}}$21. The method of recognizing and tracking multiple spatial points ofclaim 13, wherein the method of tracking the object point group isachieved by adjusting the angle (Θ,Φ) to align the Z-axis with the(X_(C),Y_(C),Z_(C)).
 22. The method of recognizing and tracking multiplespatial points of claim 6, wherein the origin of the image coordinatesystem are disposed at positions (0,h,0) (0,0,0) (−H,0,H) (H,0,H) in thevisual space coordinate system respectively, and h and H are realnumbers when the number of the 1D focusing lens module is four.
 23. Themethod of recognizing and tracking multiple spatial points of claim 13,wherein the focusing directions of the four 1D focusing lens modules areset at angles of (θ₁=0°,θ₂=0°,θ₃=90°,θ₄=−90°) and(ρ₁=90°,ρ₂=0°,ρ₃=90°,ρ₄=90°) when the number of the 1D focusing lensmodule is four.